Problem: Solve for $q$, $ -\dfrac{4q + 9}{8q} = \dfrac{10}{8q} + \dfrac{8}{2q} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $8q$ $8q$ and $2q$ The common denominator is $8q$ The denominator of the first term is already $8q$ , so we don't need to change it. The denominator of the second term is already $8q$ , so we don't need to change it. To get $8q$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ \dfrac{8}{2q} \times \dfrac{4}{4} = \dfrac{32}{8q} $ This give us: $ -\dfrac{4q + 9}{8q} = \dfrac{10}{8q} + \dfrac{32}{8q} $ If we multiply both sides of the equation by $8q$ , we get: $ -4q - 9 = 10 + 32$ $ -4q - 9 = 42$ $ -4q = 51 $ $ q = -\dfrac{51}{4}$